Are “good” tires necessary to adjust the track?

Hello experts, at our Corsa the steering head bearings were renewed. The small workshop (my trust) does not have a measuring device itself, so it went to another workshop, where it was claimed that the tyres had expired too differently to adjust the track. What has the wear of the tyres for an influence on the measurement at the track setting? M.E. is measured here on the rims. And up to a maximum of 1.5mm difference in the profile depth can not be in the stand influence the axis geometry? Or is additionally measured on a roller test bench? I can imagine an influence. I am only concerned with the setting. The workshop “with these tires” did not want to make any lane adjustment. Greetings and thanks for expert advice Michael